G22.3350-001 Honors Theory of Computation (Computational Complexity) Subhash Khot

Spring 2010

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General Information and Announcements

Homework 3 and Endterm are now available.

List of papers to read.

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Prerequisites

Prior knowledge of following materials is assumed. A brief overview of basics will be given in the first lecture. Other than this, the course should be self-contained.

• Discrete math and probability.
• Data structures : lists, trees, stacks etc.
• Algorithms, asymptotic running time, basic algorithms like breadth/depth-first search, sorting etc.
• Finite automata (deterministic and non-deterministic), regular languages, context free languages.
• Turing machines, decidability, NP-completeness, reductions.

References for this basic material are :

• M. Sipser : Introduction to the theory of computation.
• T. Cormen, C.E. Leiserson, R.L. Rivest, and C. Stein : Introduction to Algorithms (Second Edition).

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Administrative Information

Lectures: MW 3:30-4:45, WWH 312

Professor: Subhash Khot – WWH 416 , 212-998-4859, Office hours : Mon 2:30-3:30.

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Course Syllabus

The first part of the course will cover basic aspects of complexity theory. This includes complexity classes P, NP, L, NL, PSPACE, Polynomial Hierarchy, BPP, P/poly, NC, IP, AM, #P and relationships among them.

The second part of the course will cover advanced toipcs, e.g. PCPs, circuit lower bounds, communication complexity, derandomization, property testing and quantum computation. The emphasis will be on breadth rather than covering any of these topics in depth.

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Homeworks and Exams

If you are taking the course for credit, you must submit at least one of Homeworks 1,2,3 and at least one of Midterm, Endterm. Of course, if you want to

submit more than the required threshold, you are welcome!

Homework 1

Homework 2

Midterm

Homework 3

Endterm

Towards the end of the course, you will be required to read one research paper of your choosing. The list of papers/topics will be made available.

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References and Textbooks

We will not "follow" any particular textbook, but a good reference is: Arora and Barak: Computational Complexity: A Modern Approach.

A draft of this book is available at http://www.cs.princeton.edu/theory/index.php/Compbook/Draft.

You may also want to refer to :

• C.H. Papadimitriou : Computational Complexity.
• D.Z. Du and K.I. Ko : Theory of Computational Complexity.

Course notes from similar courses taught at Princeton and UC-Berkeley may be useful. See :

• Sanjeev Arora's Spring 2003 course at Princeton.
• Luca Trevisan's notes from Fall 2002 course at UC-Berkely.

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